Math, asked by aryansharma96651, 1 year ago

in a right angle triangle ABC, if b=90 degree AC= 25 cm and BC= 7 cm then find the value of tan A

Answers

Answered by Anonymous
24
b=90°
AC^2=BC^2+AB^2           (pythagoras theorem)
25^2=7^2+AB^2
625=49+AB^2
AB^2=625-49
AB^2=576
AB=√576=24
tan A= opposite/adjacent= bc/ab= 7/24
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Answered by vinod04jangid
1

Answer: The value of tan A is \frac{7}{24}.

Step-by-step explanation:

Given:In a right angle triangle ABC, ∠b=90°, AC= 25 cm and BC= 7 cm

To find: We have to find the value of tan A.

Explanation:

Step 1:It is given in right angle ΔABC, ∠B=90°,AC=25 cm BC=7 cm respectively.

Step 2:On applying pythagoras theorem in right angle ΔABC we get,

⇒              (AC)^{2} = (AB)^{2} + (BC)^{2}

⇒              (AB)^{2} = (AC)^{2}-(BC)^{2}

⇒              (AB)^{2} = (25)^{2} - (7)^{2}

⇒              (AB)^{2} = 625-49

⇒              (AB)^{2} = 576

⇒                  AB = \sqrt{576}

⇒                  AB = 24

∴    The side AB=24 cm in right ΔABC.

Step 3:As we know that in right ΔABC where ∠B=90° tan A will be the ratio of opposite side BC and adjacent side AB.

i.e.       tan A =\frac{opposite}{adjacent} =\frac{BC}{AB}

⇒         tan A = \frac{7}{24}

∴ The value of tan A is \frac{7}{24}.

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